regular hexahedron
Definition
Noun: A regular hexahedron is a three-dimensional geometric solid with six congruent square faces, twelve edges of equal length, and eight vertices. It is one of the five Platonic solids, characterized by its faces being identical regular polygons and the same number of faces meeting at each vertex.
Usage
The term is used in geometry, mathematics, and related technical fields to describe this specific, perfectly symmetrical cube. * In a geometry class: "A cube is the most common example of a regular hexahedron." * In a mathematical proof: "The properties of the regular hexahedron were used to solve the volume problem."
Advanced Usage
- In crystallography: The term can describe the cubic crystal system, where the unit cell has the shape of a regular hexahedron.
- In theoretical mathematics: It is studied for its properties of symmetry, duality (it is the dual polyhedron of the regular octahedron), and its role in the classification of regular polyhedra.
Variants and Related Words
- Cube (n): The common, everyday name for a regular hexahedron. This is the most frequently used synonym.
- Hexahedron (n): Any polyhedron with six faces. A regular hexahedron is a specific type of hexahedron.
- Platonic solid (n): Any of the five convex regular polyhedra (tetrahedron, cube, octahedron, dodecahedron, icosahedron). The regular hexahedron is one of them.
- Regular polyhedron (n): A polyhedron whose faces are congruent regular polygons and whose vertices are identical. The regular hexahedron falls under this category.
Synonyms
- Cube
- Square parallelepiped (when emphasizing its right angles and parallel faces)
Related Phrases/Idioms
- As regular as a cube: An informal phrase (not a standard idiom) sometimes used to describe something with perfect symmetry or predictability, drawing on the properties of the regular hexahedron.
Noun
-
a hexahedron with six equal squares as faces
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